A Stable Marching On-In-Time Scheme for Solving the Time-Domain Electric Field Volume Integral Equation on High-Contrast Scatterers

Abstract

A time-domain electric field volume integral equation (TD-EFVIE) solver is proposed for characterizing transient electromagnetic wave interactions on high-contrast dielectric scatterers. The TD-EFVIE is discretized using the Schaubert-Wilton-Glisson (SWG) and approximate prolate spherical wave (APSW) functions in space and time, respectively. The resulting system of equations cannot be solved by a straightforward application of the marching on-in-time (MOT) scheme since the two-sided APSW interpolation functions require the knowledge of unknown "future" field samples during time marching. Causality of the MOT scheme is restored using an extrapolation technique that predicts the future samples from known "past" ones. Unlike the extrapolation techniques developed for MOT schemes that are used in solving time-domain surface integral equations, this scheme trains the extrapolation coefficients using samples of exponentials with exponents on the complex frequency plane. This increases the stability of the MOT-TD-EFVIE solver significantly, since the temporal behavior of decaying and oscillating electromagnetic modes induced inside the scatterers is very accurately taken into account by this new extrapolation scheme. Numerical results demonstrate that the proposed MOT solver maintains its stability even when applied to analyzing wave interactions on high-contrast scatterers. Index Terms-Band-limited interpolation, electric field volume integral equation (EFVIE), extrapolation, marching on-in-time (MOT) method, time-domain analysis, transient analysis. I. INTRODUCTION T RANSIENT electromagnetic scattering from inhomogeneous dielectric volumes residing in an unbounded background medium can be analyzed by solving the timedomain electric field volume integral equation (TD-EFVIE) [1]-[8]. First, the scattered electric field is represented as a Manuscript

An explicit MOT-TD-VIE solver for time varying media

“…For this simulation, N E = 37652, N D = 21200, Δt = 12 ps, N t = 5600, α = 0.3, p and c are the sixth order Adams-Bashforth and backward differentiation (BDF) coefficients, and the convergence threshold at Step 4 is 10 −13 . The stability of the solution is ensured using the complex-exponent extrapolation scheme developed in [7] for high contrast scatterers. Fig.…”

“…The resulting coupled system of equations is integrated in time using a P E(CE) m type linear multistep scheme. The stability of resulting explicit MOT scheme is ensured using the complex-exponent extrapolation scheme developed in [7]. Unlike the existing MOT methods, explicitness of the marching scheme allows for straightforward incorporation of the time-dependent dielectric permittvitiy.…”

An explicit MOT scheme for solving the TD-EFVIE on nonlinear and dispersive scatterers

“…Here, V m is the support of f u m (r), T i (t) = T (t − i∆t), where T (t) is the approximate prolate spherical wave function [4], used for interpolating fromD i andĒ i in order to accurately account for the time retardation in L{·}. Inserting (4a), (4b), and (4d) into (2), and testing the resulting equation with f f n (r), m = 1, .., N f at discrete times j∆t yield:…”

Parallel PWTD-Accelerated Explicit Solution of the Time-Domain Electric Field Volume Integral Equation

“…INTRODUCTION ransient analysis of electromagnetic wave interactions on electrically large inhomogeneous dielectric scatterers is called for in various applications of engineering and science ranging from the design of optoelectronic devices and broadband antenna radomes to the study of (un)intentional radiation effects on human tissue/cells [1,2]. Among simulators capable of electromagnetic characterization of such scatterers, time domain electric field volume integral equation (TD-EFVIE) solvers are rapidly gaining ground [3][4][5][6][7]. The TD-EFVIE is constructed by enforcing that the total electric field is equal to the incident electric field plus the scattered electric field radiated by the electric flux density induced throughout the scatterer.…”

“…The implicit MOT scheme require at every time step solution of the linear system [3], which is traditionally constructed upon expanding the flux density with Schaubert-Wilton-Glisson (SWG) spatial basis functions [8] and piecewise polynomial temporal basis functions [9], followed by Galerkin and point testing in space and time, respectively. In addition, modern implicit MOT-based solution of time domain surface and volume integral equations can be made low-and high-frequency stable by using computationally more expensive space-time discretization techniques, such as bandlimited time discretization [7,10], space-time Galerkin testing [11,12], quasi-Helmholtz decomposition [13,14], and highly accurate evaluation of MOT matrix elements [12,[15][16][17][18][19][20]. In contrast, the explicit MOT scheme, usually leverages pulse spatial basis functions and low order temporal basis functions and point testing both in space and time.…”